Analysis of wave propagation in sandwich plates with and without heavy fluid loading

Abstract

The paper addresses wave motions in an unbounded sandwich plate with and without heavy fluid loading in a plane problem formulation. A sandwich plate is composed of two identical isotropic skin plies and an isotropic core ply. Several alternative theories for stationary dynamics of such a plate or a beam are derived, including a formulation in the framework of a theory of elasticity applied for a core ply. ‘In-phase’ and ‘anti-phase’ wave motions (with respect to transverse deflections of skins) of a sandwich beam are analyzed independently of each other. Dispersion curves obtained by the use of ‘elementary’ theories are compared with those obtained by the use of an ‘exact’ theory (which involves the theory of elasticity in a description of wave motion in a core ply) for a plate without fluid loading. It is shown that these simplified models are capable of giving a complete and accurate description of all propagating waves in not too high-frequency range, which is sufficient in practical naval and aerospace engineering. In the case of heavy fluid loading, similar analysis is performed for ‘anti-phase’ wave motions of a beam. Two simplified theories as well as an ‘exact’ one are extended to capture fluid loading effects. A good agreement between results obtained in ‘elementary’ and ‘exact’ problem formulations is demonstrated. The role of fluid's compressibility in the generation of propagating waves in a sandwich plate is explored. It is shown that, whereas analysis of wave motions in the case of an incompressible fluid predicts an existence of two propagating waves, only one such wave exists when a fluid is sufficiently compressible. The threshold magnitude of the ratio of a sound speed in an acoustic medium to a sound speed in a skin's material is found, which separates these two regimes of wave motions for a given set of parameters of sandwich plate composition.